Paraxial designing of planar waveguide variable-index focusing elements: Part 1—lenses of circular symmetry

A paraxial ray equation is used to evaluate refractive index profiles for a family of radially symmetric planar waveguide lenses. Two cases are considered: the (theoretically) full-aperture solution, and the solution with smooth index variation (non-full-aperature case). In deriving the latter case a new method has been applied that consists of the proper choice of a continuous deflection function. Both types of index profiles are described by exceptionally simple formulas.     

New Look into the Synthesis of Polyhalogenoarylphosphanes

The present study shows new aspects of the synthesis of polyhalogenoarylphosphanes. The sterically hindered anions Ph(R)P-Y^? (1a–c, Y = O, lone pair; R = Ph, Bu^t) have been used to show the complexity of the reaction between phosphorus nucleophiles and hexahalogenobenzenes or 9-bromofluorene (E3). The Ph(Bu^t)P-O^? (1a) anion reacts with hexachlorobenzene (E1), hexafluorobenzene (E2), or E3 to give Ph(R)P(O)X (4a–c, X = F, Cl, Br) with the release of the corresponding carbanion as a nucleofuge, followed by side reactions. In contrast, the lithium phosphides Ph(R)PLi (1b,c) react with hexahalogenobenzenes to give the corresponding diphosphanes 5a,b as the main product and traces of P-arylated products, i.e., Ph(R)P-C₆X₅ (10a,b, X = Cl, F). Unexpectedly, Ph(Bu^t)PLi (1b) reacts with an excess of 9-bromofluorene to give only halogenophosphane Ph(Bu^t)P-X.     

Biosorption of toxic metals using freely suspended Microcystis aeruginosa biomass

This paper describes the potential application of a freely suspended cyanobacterial biomass of Microcystis aeruginosa as a sorption material for toxic metals, cadmium (Cd) and lead (Pb) from aqueous solutions. In order to identify the most suitable conditions for removal of these elements (concentration range: 1–20 mg L^?1), the laboratory experiments were carried out during different incubation times (1–48 h) and under various temperatures (10–40°C), pH (5–9) and with or without light irradiance. Competitive biosorption of Cd and Pb was also investigated. We found that M. aeruginosa demonstrates high efficiency in removing both of the studied metals from aqueous solutions. Sorption of Pb occurred, however, more rapidly and effectively, and was less disturbed by changes in physico-chemical conditions. Under pH=7, 25°C and light, the removal rates after 3 h and 6 h of incubation, were 90–100% for Pb and 79.5–100% for Cd, respectively. The co-occurrence of the metals decreased the rate of metal biosorption. Pb was sequestered preferentially over Cd. From the results we conclude that freely suspended M. aeruginosa can constitute a promising low-cost, easy-producible biosorbent material for toxic metals in contaminated wastewater.      

Elongation method with intermediate mechanical and electrostatic embedding for geometry optimizations of polymers

The elongation method with intermediate mechanical and electrostatic embedding (ELG-IMEE) is proposed. The electrostatic embedding uses atomic charges generated by a charge sensitivity analysis (CSA) method and parameterized for three different population analyses, namely, the Merz–Singh–Kollman scheme, the charge model 5, and the atomic polar tensor. The obtained CSA models were tested on two model systems. Test calculations show that the electrostatic embedding provides several times of decrease in the difference of energies of testing and reference calculations in comparison with the conventional elongation approach (ELG). The mechanical embedding is implemented in a combination of the conventional elongation method and the ONIOM approach. Moreover, it was demonstrated that the geometry optimization with the ELG-IMEE reduces the errors in the optimized structures by about one order in root-mean-square deviation, when compared to ELG.     

Sturmian Ground States in Classical Lattice–Gas Models

Journal of Statistical Physics - We construct for the first time examples of non-frustrated, two-body, infinite-range, one-dimensional classical lattice–gas models without periodic...     

Impact of subgrid fluid turbulence on inertial particles subject to gravity

Two-phase turbulent flows with the dispersed phase in the form of small, spherical particles are increasingly often computed with the large-eddy simulation (LES) of the carrier fluid phase, coupled to the Lagrangian tracking of particles. To enable further model development for LES with inertial particles subject to gravity, we consider direct numerical simulations of homogeneous isotropic turbulence with a large-scale forcing. Simulation results, both without filtering and in the a priori LES setting, are reported and discussed. A full (i.e. a posteriori) LES is also performed with the spectral eddy viscosity. Effects of gravity on the dispersed phase include changes in the average settling velocity due to preferential sweeping, impact on the radial distribution function and radial relative velocity, as well as direction-dependent modification of the particle velocity variance. The filtering of the fluid velocity, performed in spectral space, is shown to have a non-trivial impact on these quantities.     

Flow of Emulsions Stabilized by Polymers Through Packed Bed

Transport in Porous Media - In this study, we present the results of measurements of pressure drops during the flow of emulsions stabilized by carboxymethylcellulose sodium salt (NaCMC), xanthan...     

Hamel‐isomorphic images of the unit ball

In this article we consider linear isomorphisms over the field of rational numbers between the linear spaces ?² and ?. We prove that if f is such an isomorphism, then the image by f of the unit disk is a strictly nonmeasurable subset of the real line, which has different properties than classical non‐measurable subsets of reals. We shall also consider the question whether all images of bounded measurable subsets of the plane via a such mapping are non‐measurable (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Towards uniqueness of degenerate axially symmetric Killing horizon

For near horizon geometry we examine the linearized equations around extremal Kerr horizon (which is a unique axially symmetric near horizon geometry) and give some arguments towards stability of this horizon with respect to generic (non-symmetric) linear perturbation of near horizon geometry. The result is also applicable for other situations like Kundt’s class spacetimes or isolated horizons.     

Matrix-free interior point method for compressed sensing problems

We consider a class of optimization problems for sparse signal reconstruction which arise in the field of compressed sensing (CS). A plethora of approaches and solvers exist for such problems, for example GPSR, FPC_AS, SPGL1, NestA, $\mathbf{\ell _1\_\ell _s}$ , PDCO to mention a few. CS applications lead to very well conditioned optimization problems and therefore can be solved easily by simple first-order methods. Interior point methods (IPMs) rely on the Newton method hence they use the second-order information. They have numerous advantageous features and one clear drawback: being the second-order approach they need to solve linear equations and this operation has (in the general dense case) an ${\mathcal {O}}(n^3)$ computational complexity. Attempts have been made to specialize IPMs to sparse reconstruction problems and they have led to interesting developments implemented in $\mathbf{\ell _1\_\ell _s}$ and PDCO softwares. We go a few steps further. First, we use the matrix-free IPM, an approach which redesigns IPM to avoid the need to explicitly formulate (and store) the Newton equation systems. Secondly, we exploit the special features of the signal processing matrices within the matrix-free IPM. Two such features are of particular interest: an excellent conditioning of these matrices and the ability to perform inexpensive (low complexity) matrix–vector multiplications with them. Computational experience with large scale one-dimensional signals confirms that the new approach is efficient and offers an attractive alternative to other state-of-the-art solvers.